Question

the cost of 4 red pens and 8 black pens is rs. 84. the cost of 7 red pens and 5 black pens is rs. 93; find the total cost of 3 red pens and 7 black pens.

Answer 1

let the cost of one red pen be x and one black pen be y
4x+8y=84
x+2y=21 ( take 4 as common)
(mark it as equation 1)
and 7x+5y=93. (equation 2)
then multiply eq.1 by 7 and eq.2 by 1 so as to make one of the similar variable's coefficient equal
solve it by using elimination method
after multiplying,we'll get
7x+14y=147 (eq1)
7x+5y=93 (eq2)
subtract 2nd from 1st
7x from both the equation will be cancelled and we'll get 9y=44
y=44/9=4.8
then x+2×4.8=21 (from 1)
x+9.6=21
x=21-9.6=11.4
now cost of one red pen is rs 11.4
so cost of 3 red pens=rs 34.2
and similarly cost of 7 black pens= 7×4.8=rs 33.6